The value of the determinant | , * 20 c 0& b^3 - a^3 & c^3 - a^3 … - Vidyadip

MCQ

The value of the determinant $\left| {\,\begin{array}{*{20}{c}}0&{{b^3} - {a^3}}&{{c^3} - {a^3}}\\{{a^3} - {b^3}}&0&{{c^3} - {b^3}}\\{{a^3} - {c^3}}&{{b^3} - {c^3}}&0\end{array}\,} \right|$ is equal to

A
${a^3} + {b^3} + {c^3}$
B
${a^3} - {b^3} - {c^3}$
✓
$0$
D
$ - {a^3} + {b^3} + {c^3}$

✓

Answer

Correct option: C.

$0$

c
(c) $\left| {\,\begin{array}{*{20}{c}}0&{{b^3} - {a^3}}&{{c^3} - {a^3}}\\{{a^3} - {b^3}}&0&{{c^3} - {b^3}}\\{{a^3} - {c^3}}&{{b^3} - {c^3}}&0\end{array}\,} \right|$

$({b^3} - {a^3})({c^3} - {a^3})\left| {\,\begin{array}{*{20}{c}}0&1&1\\{{a^3} - {b^3}}&1&1\\{{a^3} - {c^3}}&1&1\end{array}\,} \right| = 0$

$[{C_2} \to {C_2} - {C_1}$ and ${C_3} \to {C_3} - {C_1}]$ and then taking out common

$({b^2} - {a^3})$ from $II^{nd}$ column and ( ${c^3} - {a^3}$) from $III^{rd}$ column].

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 3 and 4 . determinant and metrices→3 and 4 . determinant and metrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The moment about the point $M( - 2,\,4,\, - 6)$ of the force represented in magnitude and position by $\overrightarrow {AB} $ where the points $A$ and $ B$ have the co-ordinates $(1,\,2,\, - 3)$ and $(3,\, - 4,\,2)$ respectively, is

$\sin^{-1}\Big(\frac{-1}{2}\Big)$

$\frac{\pi}{3}$
$-\frac{\pi}{3}$
$\frac{\pi}{6}$
$-\frac{\pi}{6}$

The radius of a sphere is changing at the rate of $0.1\text{cm}/\sec.$ The rate of change of its surface area when the radius is 200cm is:

$8\pi\text{ cm}^2/\sec.$
$12\pi\text{ cm}^2/\sec.$
$160\pi\text{ cm}^2/\sec.$
$200\text{cm}^2/\sec.$

If $\omega $ is a cube root of unity and $\Delta = \left| {\begin{array}{*{20}{c}}1&{2\omega }\\\omega &{{\omega ^2}}\end{array}} \right|$, then ${\Delta ^2}$ is equal to

If a > 0 and discriminant of ax² + 2bx + c is negative, then $\triangle=\begin{vmatrix}\text{a}&\text{b}&\text{ax}+\text{b}\\\text{b}&\text{c}&\text{bx}+\text{c}\\\text{ax}+\text{b}&\text{bx}+\text{c}&0\end{vmatrix}$ is:

Positive
(ac - b²)(ax² + 2bx + c)
Negative
0

Choose the correct answer from the given four option.
The order and degree of the differential equation $\frac{\text{d}^2\text{y}}{\text{d}\text{x}^2}+\Big(\frac{\text{d}\text{y}}{\text{d}\text{x}}\Big)^{\frac{1}{4}}+\text{x}^{\frac{1}{5}}$ respectively, are:

2 and 4
2 and 2
2 and 3
3 and 3

Evaluate: $\int[\sin (\log x)+\cos (\log x)] d x$

$\sin [{\cot ^{ - 1}}(\cos {\tan ^{ - 1}}x)] =$

The probability that a leap year will have 53 fridays or 53 Saturdays is.

$\frac{2}{7}$
$\frac{3}{7}$
$\frac{4}{7}$
$\frac{1}{7}$

A function $y = f (x)$ satisfies the condition $f '(x) sin x + f (x) cos x = 1, \, f (x)$ being bounded when $x \rightarrow 0.$ If $I = \int\limits_0^{\frac{\pi }{2}} {{\rm{f}}\,(x)\,dx} $ then